Men and women in colourful dresses formed long queues outside temporary polling booths in a Buddhist temple in Dharamsala, a town in Indias Himalayan foothills where a community of Tibetans lives in exile with the Dalai Lama.
The second such election follows a decision by the Dalai Lama, the 80-year-old Nobel Peace Laureate, to relinquish his political authority and vest it in a democratic system that ould outlast him.
China does not recognise the government that represents more than 100,000 exiled Tibetans living mainly in India, Nepal and Bhutan.
Concern about the spiritual leaders health, after his admission to a U.S. hospital this year for treatment, has reinforced the importance of the vote to keeping the issue of Tibet alive.
The "Sikyong", or elected leader, will be solely responsible for political and diplomatic decisions, as the charismatic monk steps back from the limelight amid uncertainty over how his successor will be chosen.
Tibetan Buddhism holds that the soul of a senior lama is reincarnated in the body of a child after he dies. China says it must sign off on the reincarnation of the Dalai Lama, who fled into exile in 1959 after a failed uprising.
The contest will decide who leads the parliament of the Central Tibetan Administration (CTA) in Dharamsala.
Exiled Tibetans consider the CTA to be their legitimate government, but no country recognises it. China has lobbied to sideline the Dalai Lama from the international circuit, although he did address an audience in Geneva last week despite those efforts.
Editor: Priyambodo RH
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